Senate Democrats and Republicans have reached an agreement on a process that would avert the "nuclear option" by allowing up or down votes on President Obama's executive nominees, according to Senate Democratic and Republican leadership aides.

The deal, reached Tuesday morning by Republican Sen. John McCain and Democratic Sen. Chuck Schumer, would allow a vote today on Richard Cordray, the nominee to head the Consumer Financial Protection Bureau. It would also clear the way for votes on Labor secretary nominee Thomas Perez, EPA nominee Gina McCarthy and Export-Import Bank nominee Fred Hochberg.

The deal calls for the two controversial National Labor Relations Board nominees, Richard Griffin and Sharon Block, to be withdrawn and two new nominees to be named. Republicans will not block the two new nominees. Democrats have not agreed to take future nuclear option threats off the table.

The White House has not responded to a request for comment.

By agreeing to end debate on Cordray, Republicans relented on their demand that Democrats restructure the bureau before they would allow Cordray to head it.

The deal represents a way forward after Republicans and Democrats in the chamber had a standoff over nominations, causing Reid to threaten a change to filibuster rules, widely known as the "nuclear option." Senators gathered for a rare full-chamber meeting behind closed doors on Monday, but little progress was reported.

On the floor Tuesday morning, Democratic Senate Majority Leader had signaled that a compromise was in the works saying, "I think we see a way forward that will be good for everybody. … This is not a time to flex muscles." Reid also gave a shout out to McCain, crediting him for bringing the two sides together.

But there are still more talks ahead. Reid said he plans to talk to Vice President Biden and Sens. Patty Murray and Schumer. "We're going to have caucuses today. We'll explain in more detail the direction we're headed. I think everyone will be happy," Reid said.

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